Nana has a water purifier that filters $\dfrac13$ of the contaminants each hour. She used it to purify water that had $\dfrac12$ kilogram of contaminants. Write a function that gives the remaining amount of contaminants in kilograms, $C(t)$, $t$ hours after Nana started purifying the water. $C(t)=$
Explanation: If $\dfrac{1}{3}$ of the contaminants are filtered out each hour, that means $\dfrac{2}{3}$ of the contaminants remain each hour. So each hour, the amount of contaminants is multiplied by a factor of $\dfrac{2}{3}$. If we start with the initial amount, $\dfrac12$ kilogram, and keep multiplying by $\dfrac{2}{3}$, this function gives us the remaining amount of contaminants $t$ hours after Nana started purifying the water: $C(t)=\dfrac12\left(\dfrac{2}{3}\right)^t$